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Thread: Process to find variable

  1. #1
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    Process to find variable

    Process to find variable-math-help.png
    Hi,

    Based on the info in the attached image, how would i be best going about finding the value for kappa?

    The value for kappa is given as 2d^2k, but I'm unsure how it comes to that.

    Thanks,

    Ling-pau
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  2. #2
    Junior Member Cervesa's Avatar
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    Re: Process to find variable

    As the front end of the car dips down a small angle $\theta$, the linear displacement, $\Delta s$, of spring #1 (a stretch) is approx $d \cdot \theta \implies F_{s_1} = -k \Delta s = -k d \theta$.

    The same happens at spring #2 (a compression), so $F_{s_2} = -k d \theta$.

    Overall torque on the platform is $\tau = d \times 2F = d \cdot (-2k d\theta) = \color{red}{-2kd^2} \theta = \color{red}{-\kappa} \theta$
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  3. #3
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    Re: Process to find variable

    Nice one, thank you. Makes much more sense now!
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